(50 points) At a certain high school, 15 students play stringed instruments and 20 students play brass instruments. Five students play neither stringed nor brass instruments. What is the probability that a randomly selected student plays both a stringed and a brass instrument?

Step-by-stepP(A\cup B)= 0.875

From the diagram, none of the students play both instruments.

This means the two events are mutually exclusive.

P(A\cup B)=P(A)+P(B)

The number of people playing instruments is 20.

P(A\cup B)= \frac{20}{40}  +  \frac{15}{40}

P(A\cup B)= \frac{35}{40}

P(A\cup B)= 0.875

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22 dimes and 9 nickels

step-by-step explanation: